On nonresonance impulsive functional nonconvex valued differential inclusions
Benchohra, Mouffak ; Henderson, Johnny ; Ntouyas, Sotiris K.
Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002), p. 595-604 / Harvested from Czech Digital Mathematics Library

In this paper a fixed point theorem for contraction multivalued maps due to Covitz and Nadler is used to investigate the existence of solutions for first and second order nonresonance impulsive functional differential inclusions in Banach spaces.

Publié le : 2002-01-01
Classification:  34A37,  34A60,  34G20,  34G25,  34K25,  34K45
@article{119350,
     author = {Mouffak Benchohra and Johnny Henderson and Sotiris K. Ntouyas},
     title = {On nonresonance impulsive functional nonconvex valued differential inclusions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {43},
     year = {2002},
     pages = {595-604},
     zbl = {1090.34006},
     mrnumber = {2045783},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119350}
}
Benchohra, Mouffak; Henderson, Johnny; Ntouyas, Sotiris K. On nonresonance impulsive functional nonconvex valued differential inclusions. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) pp. 595-604. http://gdmltest.u-ga.fr/item/119350/

Bainov D.D.; Simeonov P.S. Systems with Impulse Effect, Ellis Horwood Ltd., Chichister, 1989. | MR 1010418 | Zbl 0714.34083

Benchohra M.; Eloe P. On nonresonance impulsive functional differential equations with periodic boundary conditions, Appl. Math. E.-Notes 1 (2001), 65-72. (2001) | MR 1833839 | Zbl 0983.34077

Benchohra Mk.; Henderson J.; Ntouyas S.K. On nonresonance impulsive functional differential inclusions with periodic boundary conditions, Intern. J. Appl. Math. 5 (4) (2001), 377-391. (2001) | MR 1852836 | Zbl 1038.34083

Benchohra M.; Henderson J.; Ntouyas S.K. On nonresonance second order impulsive functional differential inclusions with nonlinear boundary conditions, Canad. Appl. Math. Quart., in press. | Zbl 1146.34055

Castaing C.; Valadier M. Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics, vol. 580, Springer-Verlag, Berlin-Heidelberg-New York, 1977. | MR 0467310 | Zbl 0346.46038

Covitz H.; Nadler S.B., Jr. Multivalued contraction mappings in generalized metric spaces, Israel J. Math. 8 (1970), 5-11. (1970) | MR 0263062

Deimling K. Multivalued Differential Equations, Walter de Gruyter, Berlin-New York, 1992. | MR 1189795 | Zbl 0820.34009

Dong Y. Periodic boundary value problems for functional differential equations with impulses, J. Math. Anal. Appl. 210 (1997), 170-181. (1997) | MR 1449515 | Zbl 0878.34059

Gorniewicz L. Topological Fixed Point Theory of Multivalued Mappings, Mathematics and its Applications, 495, Kluwer Academic Publishers, Dordrecht, 1999. | MR 1748378 | Zbl 1107.55001

Hu Sh.; Papageorgiou N. Handbook of Multivalued Analysis, Volume I: Theory, Kluwer Academic Publishers, Dordrecht, Boston, London, 1997. | MR 1485775 | Zbl 0887.47001

Lakshmikantham V.; Bainov D.D.; Simeonov P.S. Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989. | MR 1082551 | Zbl 0719.34002

Nieto J.J. Basic theory for nonresonance impulsive periodic problems of first order, J. Math. Anal. Appl. 205 (1997), 423-433. (1997) | MR 1428357 | Zbl 0870.34009

Samoilenko A.M.; Perestyuk N.A. Impulsive Differential Equations, World Scientific, Singapore, 1995. | MR 1355787